Stuckey was born in Cayce, South Carolina. He attended Airport High School in West Columbia, South Carolina. While there from 1972-76 he played middle linebacker and tight end.
Stuckey attended Clemson University, and played for the Clemson Tigers football team from 1976 to 1979. As a senior in 1979, he earned consensus first-team All-American honors.
He was drafted in the first round of the 1980 NFL Draft by the 49ers. He was a member of the San Francisco 49ers Super Bowl XVI and Super Bowl XIX winning teams. One of his more notable accomplishments was sealing a victory over the Dallas Cowboys in the 1981 NFC title game by recovering a fumble from quarterback Danny White with less than thirty seconds left in the game. However, this is not well known to most NFL fans, as it was preceded by The Catch, which was caught by his college teammate Dwight Clark, one of the most famous plays in NFL Lore.
Recently, Stuckey has been featured on several national advertisements for Nutrisystem, along with many other ex-NFL players. Stuckey has lost more than 60 pounds on the NutriSystem diet.